Gordon Erlebacher's Math Page

Gordon Erlebacher
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Ph.D., Columbia University, USA, 1983

Detailed description of research

Fluid Dynamics
In recent years, my interests have focused on the numerical simulation of turbulent flows with subgrid scale models. Numerical techniques used include discontinous Galerkin on unstructured meshes, spectral methods, and high order compact methods. Flows of interest include compressible isotropic turbulence and the interaction of shocks with organized structures.

Visualization of time-dependent vector fields
Aside from scalar fields, vector fields are one of the most important quantities computed. Examples include the velocity field (or vorticity) in fluid dynamics, and the electric and magnetic fields in electromagnetism.
The display of time-dependent vector fields in a meaningful fashion without sacrificing user interactivity is a continuing challenge. Together with Prof. Hussaini and Bruno Jobard (Postdoc), I am currently investigating the use of fast convolution methods (based on graphics hardware and software) to perform interactive animations of two-dimensional time-dependent vector fields. Extensions to 3-D are being considered. Techniques to avoid sensory overload will be developed.

Hand held devices for human-computer interaction Large, high resolution displays with are gaining increasing popularity in industry, national laboratories and universities. They serve to improve teaching by providing visualzations not previously possible, and vastly improve the exchange of information between scientists.
Unfortunately, the means of interaction with such devices remains at best primitive. We are leveraging the wide availability of palm pilots and PocketPCs together with wireless technology to build the next generation software tools to simplify the means by which users interface with modern displays. Face Recognition Together with Eric Klassen (Mathematics), David Banks (Computer Science) and Anuj Srinivassan (Statistics, PI), we are investigating new techniques to recognize faces based on three-dimensional geometries together with facial textures (obtained from a 3D camera). Techniques investigate include global illumination, topology, statistics, and large scale computation.